Implementation method of SWAP gate in cold atom quantum bit platform

Abstract

The invention relates to a method for realizing a rapid Rydberg blocking SWAP quantum gate based on continuous modulation laser driving. According to the method, laser is continuously modulated by adopting an analytic waveform generated based on Fourier series calculation, high-coherence Rydberg state transition of atomic quantum bits is driven, and accurate atomic state regulation and control meeting the operation requirements of an SWAP quantum gate are achieved. According to the method, errors are effectively reduced by suppressing high-frequency noise, meanwhile, defects related to mechanical motion are avoided, the heating effect generated in the operation process is prevented, the connectivity and fidelity of neutral atom bits in a large-scale system are remarkably improved, and rapid and high-fidelity SWAP quantum gate operation is achieved. And the method is suitable for low Rydberg blocking intensity, can effectively resist adverse effects such as laser fluctuation, and is compatible with a buffer atom framework, so that the intensity of quantum entanglement connection is enhanced.

Description

Technical Field

[0001] The present invention relates to the field of quantum computing, and in particular to a method for realizing a SWAP gate in a cold atom quantum bit platform driven by Rydberg blockade and continuous laser modulation. Background Art

[0002] In the development of large-scale neutral atom quantum computing, a core problem is that due to the limited range of Rydberg dipole-dipole interactions, how to effectively realize entangled quantum logic gates with high connectivity and fast high fidelity has become an urgent challenge. In the prior art, although the method of mechanically transferring quantum bits in one-dimensional optical lattices (Demonstration of Quantum Brachistochrones between Distant States of an Atom, author Manolo R. Lam, Natalie Peter, Thorsten Groh, Wolfgang Alt, Carsten Robens, Dieter Meschede, Antonio Negretti, Simone Montangero, Tommaso Calarco and Andrea Alberti) can improve the connectivity between quantum bits to a certain extent, this method has significant defects, slow operation speed and easy to cause leakage of quantum states, thus affecting the efficiency and accuracy of quantum computing.

[0003] On the other hand, the optimized Rydberg CZ gate pulse (cited from Architecture for fast implementation of qLDPC codes with optimized Rydberg gates, authors C. Poole, TM Graham, MA Perlin, M. Otten, and M. Saffman) can minimize the dependence on the strength of the diatomic interaction while ensuring the high fidelity and speed of quantum operations. This progress undoubtedly opens up a new path for the realization of quantum logic gates. However, it is worth noting that the current Rydberg gate design still lacks in functional coverage, especially the failure to include the key component of the SWAP gate, which is essential for building complex quantum circuits. Summary of the invention

[0004] In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a high-speed, high-fidelity Rydberg SWAP gate design method, which not only has the characteristics of high speed and high fidelity, but also is compatible with the buffer atomic framework, achieving high connectivity when the atoms are in a static state.

[0005] The present invention aims to improve the qubit connectivity of large-scale neutral atom quantum computing platforms. By using Rydberg blockade and continuous modulation drive, a SWAP gate similar to that on superconducting computing platforms is realized, with high speed, high connectivity and high fidelity entanglement characteristics. This method is compatible with auxiliary and buffered atomic bit architectures, keeps atomic bits static, and provides an efficient and robust solution to enhance the scalability and performance of quantum computing.

[0006] The technical solution of the present invention is as follows:

[0007] A method for implementing a SWAP gate in a cold atom quantum bit platform, wherein the method comprises the following steps:

[0008] Step 1.1 Select two non-degenerate and magnetically insensitive ground states as quantum bit states |0> and |1>;

[0009] Step 1.2: Use two coherent laser beams to drive the ground state-Rydberg state transition, and set the Rabi frequencies of the two laser beams to ensure that the light intensity is evenly distributed on the control quantum bit atoms and the target quantum bit atoms;

[0010] Step 1.3 considers the Rydberg blocking effect and generates a Rabi frequency waveform that meets the SWAP gate condition by continuous laser modulation driving.

[0011] Further, the step 1.2 specifically includes:

[0012] Step 2.1: select two coherent laser beams, wherein the frequency of the first laser beam is ω0, and the frequency of the second laser beam is ω1; the frequency ω0 of the first laser beam matches the transition frequency of the quantum bit state |0> to the Rydberg state |r>, and the frequency ω1 of the second laser beam matches the transition frequency of the quantum bit state |1> to the Rydberg state |r>;

[0013] Step 2.2 ensures that the action area of ​​the two light beams is much larger than the area where all the control quantum bit atoms and the target quantum bit atoms are located, and ensures that the light intensity is evenly distributed so that the Rabi frequency is evenly distributed on the atomic bits;

[0014] Step 2.3 uses the first laser beam to excite the atom from the quantum bit state |0> to the Rydberg state |r>, and uses the second laser beam to excite the atom from the quantum bit state |1> to the Rydberg state |r>.

[0015] Further, the step 1.3 specifically includes:

[0016] Step 3.1 Describe the Rydberg blockade interaction through the quantum mechanical model of Rydberg atomic dipole interaction, and predict and adjust the dynamical behavior of the singlet and triplet states;

[0017] Step 3.2 generates a Rabi frequency waveform that meets the SWAP gate condition, ensuring that the initial and final intensities of the Rabi frequency waveform are zero and its first-order derivative with respect to time is also zero;

[0018] Step 3.3 realizes the corresponding Rabi frequency waveform by amplitude, frequency or mixed modulation, and filters out high-frequency components;

[0019] Step 3.4 regulates the phase accumulation of the atomic wave function to achieve efficient population transfer and generate a variety of SWAP phase gates.

[0020] Further, the step 3.2 specifically includes:

[0021] Step 3.2.1: Use the Fourier series coefficients [a0, a1, ..., a N ] represents the Rabi frequency of all light fields

[0022]

[0023] Step 3.2.2 determines the coefficients using direct numerical search or an optimization algorithm to generate a waveform that meets the SWAP gate conditions.

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] 1. The Rydberg blockade-based SWAP gate realized by synthetic continuous modulation drive facilitates the connection and entanglement of large-scale neutral atomic bits.

[0026] 2. Automatically trigger the diatomic dark state mechanism and improve the fidelity of the SWAP gate by filtering high-frequency noise.

[0027] 3. Quantum logic gates and buffer atom architectures that are compatible with buffer atom control without mechanical atom transport have the potential to suppress crosstalk and enhance entanglement connectivity. That is, by applying the SWAP gate between the buffer atom and the atomic bit, the buffer atom or buffer atom relay can effectively implement the SWAP gate between the quantum bits, and because the buffer atom and the quantum bit are different elements, crosstalk can be effectively avoided.

[0028] 4. When the two laser beams are parallel and propagating in the same direction, the average exchange of net atomic and photon momentum is zero, so the SWAP gate based on Rydberg blocking does not cause heating effect. On the other hand, it provides a tool to cool the quantum bits heated by arbitrary reasons in quantum logic gate operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the atomic transition link structure under single-photon drive and light-atom interaction.

[0030] Figure 2is a complete schematic diagram of the singlet and triplet states.

[0031] Figure 3 Schematic diagram of atomic bit transition dynamics under the modulation driving scheme.

[0032] Figure 4 Schematic diagram of the Rydberg blockade effect and the two-photon transition scheme.

[0033] Figure 5 It is the input-output relationship diagram of the two SWAP gate states. DETAILED DESCRIPTION

[0034] The present invention will be further described below in conjunction with the accompanying drawings and embodiments, but the protection scope of the present invention shall not be limited thereto.

[0035] In the cold atom qubit platform, two non-degenerate and magnetic field-insensitive ground states or metastable states are selected as qubit states |0> and |1> for the bit atom 1-1. Single-bit operation 1-2 can be achieved through microwave or Raman transition. Two mutually coherent laser beams are used to drive the transition from the ground state to the Rydberg state. and The laser frequencies are ω0 and ω1 respectively. Ensure that the action area of ​​the two beams is much larger than the area where all the control quantum bit atoms and target quantum bit atoms are located, and ensure that the light intensity is evenly distributed so that the Rabi frequency is evenly distributed on the atomic bits. Consider the Rydberg blockade effect of three Rydberg states, and use the quantum mechanical model of Rydberg atomic dipole interaction to describe Rydberg blockade interactions 1-3, with a blockade strength of B. Consider the singlet state in the superposition state under the diatomic basis vector and triplet The different dynamic responses of |00> and |11> are 1-4, and the wave functions of the complete dynamics involving the singlet state 2-1 and triplet state 2-2 are C singlet =[C 1- ,C 0r ,C 1r ] and C triplet =[C0,C 1+ ,C2,C r0 ,C r1 ,C rr ,C qq' ]. Use the synthesized continuous modulation drive lasers 1 and 2 to regulate the phase accumulation of the atomic bit wave function required for the SWAP phase gate, realize the coherent particle number transfer, make the quantum bit undergo coherent transitions 3-1 and 3-2, and realize the SWAP gate. The specific modulation scheme is as follows: ensure that the initial and final intensities of the Rabi frequency waveform and its first-order time derivative are both zero, and use the Fourier series coefficients [a0, a1, ..., a N ] represents the waveform of Rabi frequency The appropriate Fourier coefficients are found through numerical search or optimization algorithms to generate a Rabi frequency waveform that meets the conditions of the SWAP gate. The waveforms of the two laser beams can be of the same proportion. Then, according to the required Rabi frequency waveform, the amplitude or phase modulation of the laser or a combination of the two is used, and the high-frequency components are filtered to achieve the final output waveform. This scheme is not only applicable to single-photon transitions, but also to scheme 4-1 of two-photon ground state-Rydberg transitions. The final realization is as follows Figure 5 The input-output relationship of the SWAP gate is shown.

[0036] In order to construct a stable qubit, two non-degenerate and magnetic field-insensitive ground states or metastable states are selected to represent the qubit states |0> and |1>. This helps to reduce the interference of the external environment on the qubit state and improve the accuracy of quantum computing.

[0037] Single-bit operations 1-2 are usually achieved through microwaves or Raman transitions, both of which can effectively manipulate the state of quantum bits.

[0038] Two mutually coherent laser beams are used to drive the transition from the ground state to the Rydberg state, thereby realizing the interaction between quantum bits. The frequencies of the two laser beams are ω0 and ω1, respectively, and the light intensity is evenly distributed on the control quantum bit atom and the target quantum bit atom.

[0039] The Rydberg state is a highly excited state with a large electric dipole moment, which can produce a strong interaction, which is called the Rydberg blockade effect. In the Rydberg blockade effect of the three Rydberg states, the quantum mechanical model of the Rydberg atomic dipole interaction is used to describe the Rydberg blockade interaction 1-3, and the blocking strength B describes the strength of this interaction.

[0040] Under the diatomic basis vector, the singlet state in the superposition state and triplet The different dynamic responses of 00> and |11> are 1-4, and the wave functions of the complete dynamics involving the singlet state 2-1 and the triplet state 2-2 are C singlet =[C 1- ,C 0r ,C 1r ] and C triplet =[C0,C 1+ ,C2,C r0 ,C r1 ,C rr ,C qq' ]; Use the synthesized continuously modulated driving lasers 1 and 2 to regulate the phase accumulation of the atomic bit wave function required for the SWAP phase gate, realize the coherent particle number transfer, so that the quantum bit undergoes coherent transitions 3-1 and 3-2, and finally realizes the SWAP gate.

[0041] The specific modulation scheme is as follows:

[0042] Ensure that the initial and final intensities of the Rabi frequency waveform and its first-order time derivative are zero, using the Fourier series coefficients [a0, a1, ..., a N ] represents the waveform of Rabi frequency The appropriate Fourier coefficients are found through numerical search or optimization algorithms to generate a Rabi frequency waveform that meets the conditions of the SWAP gate. The waveforms of the two laser beams can be of the same proportion. Then, according to the required Rabi frequency waveform, the amplitude or phase modulation of the laser or a combination of the two is used, and the high-frequency components are filtered to achieve the final output waveform. This scheme is not only applicable to single-photon transitions, but also to scheme 4-1 of two-photon ground state-Rydberg transitions. The final realization is as follows Figure 5 The input-output relationship of the SWAP gate is shown.

[0043] Figure 5 The implementation of two SWAP gate schemes 5-1 and 5-2 is demonstrated, using a large-scale rubidium 87 cold atom array as an example. Figure 1 The atomic transition link structure under single-photon drive and light-atom interaction is shown. As shown in the figure, for the bit atom 1-1, two magnetic field-insensitive ground states F=1, m=0 and F=2, m=0 are selected as quantum bits |0> and |1>. Figure 4 The Rydberg blockade effect and two-photon transition scheme are demonstrated. As shown in the figure, two pairs of 480nm and 780nm lasers realize the two-photon transition 4-1 of the 89S Rydberg state. The frequencies of the two pairs of lasers are ω e1 ,ω r1 and ω e2 ,ω r2 , the corresponding detuning is Δ e1 , Δ r1 and Δ e2 , Δ r2 The Rabi frequencies of the two pairs of lasers are Ω e1 ,Ω r1 and Ω e2 ,Ω r2 , ensuring that the light field is evenly distributed on the target quantum bit atom to improve fidelity and make the equivalent Rabi frequency consistent. Use a beam splitter to make the two pairs of lasers completely overlap and irradiate the target quantum bit atom in the same direction, manage the momentum exchange between the laser and the atom, and suppress the heating effect caused by the Rydberg transition. Figure 2The wave functions of the complete singlet and triplet states involved in the transition process under Rydberg blockade are described, and the Rydberg blockade interaction 1-3 is described by the quantum mechanical model of Rydberg atomic dipole interaction, and the dynamics of singlet state 2-1 and triplet state 2-2 are predicted and controlled. The ground state of these two pairs of lasers are selected to transition to the 89S energy level, and the corresponding Rydberg dipole-dipole interaction strength is about 100-200MHz.

[0044] Using the Fourier series coefficients [a0, a1, ..., a N ] represents the Rabi frequency of all light fields Ω e1 ,Ω r1 and Ω e2 ,Ω r2 Waveform The selected reference time τ = 0.25μs. Ensure that the time from the start of the waveform t = 0 to the end of the SWAP gate operation t = t end f(0) = f(t end )=0 and f'(0)=f'(t end )=0. The appropriate Fourier coefficients of each light field are found by direct numerical search method, and the Rabi frequency waveform that meets the SWAP gate condition is obtained. The corresponding Rabi frequency waveform is realized by hybrid modulation, that is, the intensity and phase modulation of the light are combined, and the high-frequency components are filtered. Figure 3 Shows t end The coherent transition dynamics of atomic bits under the modulation driving scheme in time. For the path design of SWAP gate 5-1, the |01> state starts to experience two paths, the first one is |01>→|0r>→|00>→|r0>→|10>, and the second one is |01>→|r1>→|11>→|1r>→|10>. At the same time, the layout of bits in the coherent transition remains unchanged; for the path design of SWAP gate 5-2, starting from the |00> state, two paths are experienced, the first one is

[0045] 00>→|0r>→|01>→|r1>→|11>, and the second is |00>→|r0>→|10>→|1r>→|11>, while the |01> and 10> states keep the same proportion in the cycle. Finally, through precise waveform design and regulation, it is achieved Figure 5 The two SWAP gate schemes are shown.

[0046] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for implementing a SWAP gate in a cold atom quantum bit platform, characterized in that: The method comprises the following steps: Step 1.1 Select two non-degenerate and magnetically insensitive ground states as quantum bit states |0> and |1>; Step 1.2: Use two coherent laser beams to drive the ground state-Rydberg state transition, and set the Rabi frequencies of the two laser beams to ensure that the light intensity is evenly distributed on the control quantum bit atoms and the target quantum bit atoms; Step 1.3 considers the Rydberg blocking effect and generates a Rabi frequency waveform that meets the SWAP gate condition by continuous laser modulation driving.

2. The method for implementing a SWAP gate in a cold atom quantum bit platform according to claim 1, characterized in that: The step 1.2 specifically includes: Step 2.1: select two coherent laser beams, wherein the frequency of the first laser beam is ω0, and the frequency of the second laser beam is ω1; the frequency ω0 of the first laser beam matches the transition frequency of the quantum bit state |0> to the Rydberg state |r>, and the frequency ω1 of the second laser beam matches the transition frequency of the quantum bit state |1> to the Rydberg state |r>; Step 2.2 ensures that the action area of ​​the two light beams is much larger than the area where all the control quantum bit atoms and the target quantum bit atoms are located, and ensures that the light intensity is evenly distributed so that the Rabi frequency is evenly distributed on the atomic bits; Step 2.3 uses the first laser beam to excite the atom from the quantum bit state |0> to the Rydberg state |r>, and uses the second laser beam to excite the atom from the quantum bit state |1> to the Rydberg state |r>.

3. The method for implementing a SWAP gate in a cold atom quantum bit platform according to claim 1, characterized in that: The step 1.3 specifically includes: Step 3.1 Describe the Rydberg blockade interaction through the quantum mechanical model of Rydberg atomic dipole interaction, and predict and adjust the dynamical behavior of the singlet and triplet states; Step 3.2 generates a Rabi frequency waveform that meets the SWAP gate condition, ensuring that the initial and final intensities of the Rabi frequency waveform are zero and its first-order derivative with respect to time is also zero; Step 3.3 realizes the corresponding Rabi frequency waveform by amplitude, frequency or mixed modulation, and filters out high-frequency components; Step 3.4 regulates the phase accumulation of the atomic wave function to achieve efficient population transfer and generate a variety of SWAP phase gates.

4. The method for implementing a SWAP gate in a cold atom quantum bit platform according to claim 3, characterized in that: The step 3.2 specifically includes: Step 3.2.1: Use the Fourier series coefficients [a0, a1, ..., a N ] represents the Rabi frequency of all light fields Step 3.2.2 determines the coefficients using direct numerical search or an optimization algorithm to generate a waveform that meets the SWAP gate conditions.

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